Recent advances in bioinformatics promise rational drug-design meth-
ods which will reduce serious side-effects through the identification of en-
zymatic targets. Efficient computational methods are required to identify
the optimal enzyme-combination (i.e., drug targets) whose inhibition will
achieve the required effect of eliminating a given target set of compounds
while incurring minimal side-effects. An exhaustive evaluation of all possi-
ble enzyme combinations may become computationally infeasible for very
large metabolic networks.
*Work supported partially by ORAU (Award No: 00060845).

We formulate the optimal enzyme-combination identification problem as

an optimization problem on metabolic networks. We define a graph based

computational model of the network which encapsulates the impact of en-

zymes onto compounds. We propose a branch-and-bound algorithm, named

OPMET, to explore the search space. We develop a cost model and two en-

zyme prioritization strategies, Static OPMET and Dynamic OPMET, based

on it. Static OPMET priorities enzymes according to their impacts, such

that the most promising enzymes are inspected first for possible inclusion

in the optimal subset. Dynamic OPMET dynamically updates the priorities

as the search space is explored. We also develop two filtering strategies to

prune the search space while still guaranteeing an optimal solution. They

compute an upper bound to the number of target compounds eliminated and

a lower bound to the side-effect respectively. Our experiments on E.Coli

metabolic network show that OPMET can reduce the total search time by

several orders of magnitude as compared to the exhaustive search.

1 Introduction

In pharmaceutics, the development of every drug mainly involves target identi-

remove) be the node on top of this stack (i.e., the node to be evaluated). We check

if the damage of the current node N, d < D and whether it is a true node. There

are three cases:

Case 1: N is a true node with damage d < D. In this case, we save N as the

10

[0001,

[0110, 3, 2, True]

Figure 2: The basic OPMET strategy for a hypothetical 4-enzyme network. Enzymes
are ordered as El, E2, E3, E4. no, nl, " -, n4 are the nodes generated. The initial global
cut-offthreshold D = 10 initializedd to the total number of compounds in the network).
ni is a true solution (shown by double circle) with damage d = 5. Since d < D, D is
updated to 5. n1 is saved and the subtree rooted at n1 is pruned. The method backtracks
to no. n2, n3 are false nodes generated along the search with damage d < D. ns is a true
node with d = 2. As d < D, D is updated to 2 and the method backtracks to search the
unexplored space for solutions with d < D (indicated by the dashed edge).

current true solution and update D with the damage value of N. We then

backtrack.

Case 2: N is a true or false node with damage d > D. In this case we prune

the subtree rooted at N. We then backtrack.

Case 3: N is a false node with damage d < D. In this case, we insert N in

the active set A for backtracking purposes. We then create a new node N'

by setting e+ = 1 in N (i.e., we inhibit the enzyme Ek+ ). The resulting

node is N' = ([e,, e,2, * e,], k + 1, d', remove'). The node N' is

evaluated in the next step similarly.

Backtracking involves following steps. First we pick the top node from the ac-